Safety is often the most important requirement in robotics applications. Nonetheless, control techniques that can provide safety guarantees are still extremely rare for nonlinear systems, such as robot manipulators. A well-known tool to ensure safety is the Viability kernel, which is the largest set of states from which safety can be ensured. Unfortunately, computing such a set for a nonlinear system is extremely challenging in general. Several numerical algorithms for approximating it have been proposed in the literature, but they suffer from the curse of dimensionality. This paper presents a new approach for numerically approximating the viability kernel of robot manipulators. Our approach solves optimal control problems to compute states that are guaranteed to be on the boundary of the set. This allows us to learn directly the set boundary, therefore learning in a smaller dimensional space. Compared to the state of the art on systems up to dimension 6, our algorithm resulted to be more than 2 times as accurate for the same computation time, or 6 times as fast to reach the same accuracy.

翻译：安全性通常是机器人应用中最关键的要求。然而，对于机器人操作臂等非线性系统，能够提供安全保证的控制技术仍极为罕见。确保安全的著名工具是生存核，即能够保证安全的最大状态集合。遗憾的是，对于非线性系统，计算该集合通常是极其困难的。已有文献提出了多种数值近似算法，但这些算法普遍面临维数灾难问题。本文提出了一种新的机器人操作臂生存核数值近似方法。该方法通过求解最优控制问题来计算确保位于集合边界上的状态，从而直接学习集合边界，即在更低维空间中进行学习。与当前最高水平方法相比，在维度不超过6的系统上，我们的算法在相同计算时间内准确率提升超过2倍，或为达到相同精度所需计算速度提高6倍。